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The function H(t) = -16t2 + vt + s shows the height H (t), in feet, of a projectile launched vertically from s feet above the ground after t seconds. The initial speed of the projectile is v feet per second. Part A: The projectile was launched from a height of 100 feet with an initial velocity of 60 feet per second. Create an equation to find the time taken by the projectile to fall on the ground. (2 points) Part B: What is the maximum height that the projectile will reach? Show your work. (2 points) Part C: Another object moves in the air along the path of g(t) = 20 + 38.7t where g(t) is the height, in feet, of the object from the ground at time t seconds. Use a table to find the approximate solution to the equation H(t) = g(t), and explain what the solution represents in the context of the problem? [Use the function H(t) obtained in Part A, and estimate using integer values] (4 points) Part D: Do H(t) and g(t) intersect when the projectile is going up or down, and how do you know? (2 points)
We are given the function with constants for the height and speed. Can you plug them in?
H(t)=-16t^2+100(60)+s would that right @JoannaBlackwelder
Close, I get: 16t^2 + 60t +100
can you help me with parts c and d @JoannaBlackwelder
Sure, can you make a table of values of H(t) and g(t)?
g(t) h(t) 1 58.7 144 2 97.4 156 3 136.1 136 4 174.8 84
is that ok @JoannaBlackwelder
Yep, that's a good start? Do you know what we are looking for in the table?
the point were h(t)=g(t)
Yep, the point or points. :-) Do you see one so far?
at 3 they are the closest
Yep, I think we can say they are about the same at t=3. :-) So, what does that represent in the problem?
the point were they intersect?
Yep, that would be the point where the two objects would hit each other. :-)
for part d how do I know whether or not it is going down or up?
It would be going up if it is before the vertex, down if it is after.
Since the parabola is upside down
it would be going down ,right?
can you help me with a couple more equations.
Possibly. But open a new question, please. And tag me :-)